A089831 - OEIS

A089831

Triangle T(n,m) (read as T(1,1); T(2,1), T(2,2); T(3,1), T(3,2), T(3,3);) Number of distinct non-recursive Catalan Automorphisms whose minimum clause-representation requires examination of n nodes in total, divided into m non-default clauses.

1, 10, 0, 115, 10, 0, 1666, 139, 0, 0, 30198, 2570, 0, 0, 0, 665148, 47878, 904, 0, 0, 0, 17296851, 1017174, 20972, 0, 0, 0, 0

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..28.

A. Karttunen, C-program for computing the initial terms of this sequence

A. Karttunen, Prolog-program which illustrates the construction of non-recursive Catalan bijections with clause-representations

A. Karttunen, Catalan Automorphisms

EXAMPLE

...... Triangle............................ Row sums

........1........................................1

.......10.......0...............................10

......115......10...0..........................125 = 5^3

.....1666.....139...0....0....................1805 = 5*19^2

....30198....2570...0....0...0...............32768 = 32^3 = 8^5

...665148...47878...904..0...0...0..........713930

.17296851.1017174.20972..0...0...0...0....18334997

T(1,1)=1, as there is just one non-identity, non-recursive Catalan bijection with a single non-default clause opening a single node, namely A089840[1]=A069770.

T(2,1)=10, as there are the following non-recursive Catalan bijections (rows 2-11 of A089840): A072796, A089850, A089851, A089852, A089853, A089854, A072797, A089855, A089856, A089857, whose minimum clause-representation consists of a single non-default clause that opens two nodes.

T(3,2)=10, as there are the following non-recursive Catalan bijections (rows 12-21 of A089840): A074679, A089858, A073269, A089859, A089860, A074680, A089861, A073270, A089862, A089863, whose minimum clause-representation consists of a two non-default clauses with total 3 nodes opened.

CROSSREFS

First column: A089833. Row sums: A089832. Row sums excluding the first column: A089834.

Sequence in context: A285780 A285536 A285477 * A221414 A326719 A070190

Adjacent sequences: A089828 A089829 A089830 * A089832 A089833 A089834

KEYWORD

nonn,tabl

AUTHOR

Antti Karttunen, Dec 05 2003

STATUS

approved